Grade Six Mathematics
Greetings, students! It's great to have you back. I hope you all had a fantastic week. In our previous session, we delved into the four operations of numbers. Now, let's shift our attention to understanding the order of operations this week.
Mathematical Operations
The term "mathematical operations" refers to the actions performed on the provided numbers. As we all know, the primary operations include:
• addition (+);
• subtraction (-);
• multiplication (x);
• division (÷).
Hence, when you see something like...
7 + (6 × 2 + 3)
... What part should you calculate first?
Start at the left and go to the right? Or go from right to left?
Don’t worry, let’s find out!
In ancient times, individuals collectively established a set of guidelines for performing calculations, now known as the order of operations.
Order of Operation
The order of operations serves as a guideline outlining the proper sequence of steps to evaluate a mathematical expression. It dictates the order in which specific operations should be carried out, starting with brackets and concluding with addition and subtraction.
BODMAS is an acronym designed to aid in recalling the sequence of mathematical operations, guiding you on the proper order for solving mathematical problems.
Order of Operations BODMAS
• B stands for Brackets ( ), { }, [ ]
• O stands for Order
• D stands for Division (÷)
• M stands for Multiplication (×)
• A stands for Addition (+)
• S stands for Subtraction (-)
Let us look at an example using the order by BODMAS. Example 1.
Solve: 4 + 3 x 2
According to BODMAS:
-the multiplication must be completed first (3 x 2= 6)
-and then the addition (4 + 6 = 10).
Therefore, the correct answer is 10.
Example 2 (Expressions with brackets)
Expression: 3 × (2 + 5)
According to BODMAS,
-we simplify the bracket first; (2+5) = 7
-then we multiply the product by 3;
Solution: 3 × (7) = 21
Boys and girls do you understand? If not, please thoroughly review the examples provided earlier. Having explored the sequence of mathematical operations, let's now work the following problems. .
Exercise 1
Solve the following mathematical expressions, using
BODMAS.
a. 20 − 5 + 3
b. 2 × (14÷ 2)
c. 18 − 4 × 4
d. 1 + 8 - 3
e. 24 ÷ (4 + 2)
f. 9 − (4 × 2)
g. 25 ÷ (4 + 1)
h. 4 × 8 + 10
i. 12 + 3 - 10
j. (5× 5) ÷ 2
Great job!
Order of operations in worded problems
Word problems involve the translation of sentences into equations, followed by the solution of these equations.
Example #1:
Sylvia bought 4 bananas for $50 each, and 1 apple for $80. Write a numerical expression to represent this situation and then find the total cost.
Solution
No. of bananas purchased=4
Cost of 1 banana= $50
No. of apples purchased= 1
Cost of 1 apple= $80
Therefore, total cost of 4 bananas + 1 apple
= 4 × 50 + 80
= 200 + 80
= $280
Example #2:
Robert bought 2 burgers for $3.50 each and 3 medium French fries for $1.20 each. Write a numerical expression to represent this situation and then find the cost.
Solution
2 × 3.50 + 3 × 1.20
= 7 + 3.60
= $10.60
Ok, students. Now that we've learned how to represent worded problems using mathematical equations, let's go ahead and work through a few of them.
Exercise 2
Solve the following using BODMAS.
1. Suppose you went to purchase five pepperoni pizzas that cost $50 each, and you want to split the total cost among 10 people evenly. Find out how much each person needs to pay.
2. If 50 is divided by the sum of 4 and 6, then subtracted from 10, what will be the final answer?
3. Sarah bought 3 skirts for $50 each and 2 belts for $30 each. Write a numerical expression to represent this situation.
Well done, everyone! That concludes today's session. Return next week for the solutions to this week's problems. Wishing you all a productive and blessed week ahead, boys and girls!